MinT - Best Known (181, 181+46, s)-Nets in Base 2

Best Known (181, 181+46, s)-Nets in Base 2

(181, 181+46, 260)-Net over F₂ — Constructive and digital

Digital (181, 227, 260)-net over F₂, using

t-expansion [i] based on digital (180, 227, 260)-net over F₂, using
- 5 times m-reduction [i] based on digital (180, 232, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 58, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(181, 181+46, 554)-Net over F₂ — Digital

Digital (181, 227, 554)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(181, 181+46, 8786)-Net in Base 2 — Upper bound on s

There is no (181, 227, 8787)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 215 947336 255968 898831 007781 682669 099734 241387 634039 061140 730761 947840 > 2²²⁷ [i]